THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE

초록

It has been conjectured that, on a compact 3-dimensional orientable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker s(g)'* not equal 0, which generalizes the previous partial results.

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